Pilot symbols in communication systems

ABSTRACT

This invention relates to signal processing in telecommunications, particularly but not exclusively for use in wireless TDMA systems. In particular, the invention concerns methods for use in communication systems making use of pilot symbols. The invention provides a method of placing pilot symbols in a data stream for telecommunication systems, wherein the pilot symbols are spaced in time using a range of different intervals between symbols. The intervals between the pilot symbols are substantially fractal in nature, the distribution of pilot symbols involving repetitions of irregular groupings of pilot symbols in the data stream. Preferably, the irregular groupings of pilot symbols are irregularly spaced in the data stream. The invention also provides a method and means for acquiring the time and frequency offset of a packet of data by using pilot symbols distributed within the packet as defined above.

RELATED APPLICATIONS

The present application is a U.S. National Phase Application ofInternational Application PCT/AU2003/001484 (filed Nov. 7, 2003) whichclaims the benefit of Australian Patent Application No. 2002952566(filed Nov. 7, 2002), all of which are herein incorporated by referencein their entirety for all purposes.

FIELD OF THE INVENTION

This invention relates to signal processing in telecommunications,particularly but not exclusively for use in wireless TDMA systems. Inparticular, the invention concerns methods for use in communicationsystems making use of pilot symbols.

BACKGROUND TO THE INVENTION

Pilot symbol assisted modulation (PSAM) is a known method used to reduceeffects of fading and other distortion factors in mobile communications,by periodically inserting known pilot symbols in the signal data stream.Since the transmitted pilot symbols are known, the receiver can make useof these regularly spaced pilot symbols to derive the amplitude andphase reference of the received signal. Channel estimators are used todetermine the amplitude and phase reference at the known pilot symbols,providing correction factors that can then be interpolated and appliedto the other symbols (data symbols) in the signal. There is, in general,a tradeoff between the complexity of the acquisition algorithm and itsrobustness. Two types of algorithms used for frequency acquisition aredifferential decoding and coherent correlation (see below).

The robustness of frequency estimation for a data packet in noisedepends on the pattern of pilot symbols throughout the packet. The mostrobust methods use the Fourier Transform. In this method, the datasymbols are identified and removed, leaving the pilot symbols. A FourierTransform (typically, the Fast Fourier Transform—FFT) is then applied tothe resulting packet in order to identify the maximum-likelihoodfrequency.

Pilot symbols do not carry any data, and it is therefore necessary tokeep them to as few as possible. However, too few pilot symbols canresult in performance degradation due to poor channel estimation. Thetrade-off between pilot symbol spacing and the symbol error rate istherefore an important consideration for system of this type.

The dominant method of TDMA packet acquisition uses contiguous blocks ofpilot symbols, known as Unique Words (UW) often coded with binary phaseshift keying (BPSK) to allow identification of the packet's time offset.Fast algorithms have been developed for UW packet acquisition.

If a single UW is used alone, the frequency acquisition is poor. Methodshave therefore been developed to spread pilot symbols over the length ofthe packet. Two methods are commonly used to improve frequency offsetestimation in such packet acquisition:

-   1. Pilot symbols regularly spaced throughout the packet. Once the    contiguous block of UWs has been used to establish the packet's    timing, the channel can be sampled at regular intervals and the    pilot symbols throughout the packet may be used to identify the    frequency to an acceptable resolution. This divides the UW into two    parts, each used for different tasks, which is not computationally    efficient. Ideally, all pilot symbols should be used for both time    and frequency acquisition.-   2. Two UWs, one placed at either end of the packet. The phase    between the leading and trailing pilot symbol UWs gives a precise    frequency estimate. However, such methods can tend to distinguish    poorly between certain frequency alternatives, as no pilot symbol    data is available throughout the bulk of the packet.

Coherent correlation methods are comparatively fast. In such techniques,the majority of the pilot symbols are in a UW at the front of thepacket. A frequency offset is applied to the UW symbols before they aresummed. However, if the frequency offset is not close to the signal'sactual frequency, symbols in the UW can cancel one another, and the SNRwill thus be significantly decreased. To overcome this, coherentcorrelation must be repeated at a number of different frequency offsets,such that at least one frequency option is sufficiently close to theactual frequency. This repetition increases the complexity, and thetechnique is less robust than the Fourier Transform frequency responsemethod described above.

Differential decoding methods are also comparatively fast, and they neednot deal with coherence issues. However, they decrease the effective SNRby multiplying noise data symbols together. To overcome this,differential decoding must be repeated at several differenttime-offsets, which once again increases the algorithm complexity. Thetechnique cannot improve on a performance dictated by the pattern ofpilot symbols.

Methods have been proposed in the past for pilot structures relying onnon-uniform spacing, such as that postulated in ‘A study of Non-UniformPilot Spacing for PSAM’, Lo, H., Lee, D. and Gansman, J. A., IEEE 2000,Proc ICC International Conference on Communications, Volume 1, 18-22Jun. 2000, pp. 322-325. This paper examines a number of alternativestructures, and concludes that performance can theoretically be improvedwithout increasing the number of pilot symbols by using non-uniformdistributions, especially at high Doppler rates and in the presence ofan unknown frequency offset. However, the paper does not consideroptimisation, and the non-uniform structures considered are in factrepeating regular patterns.

There is scope to improve the robustness of frequency acquisition byimproved selection of the pattern of pilot symbols.

SUMMARY OF THE INVENTION

It is an object of the invention to at least partially address theinconveniences of the prior art, and to provide a useful alternative toexisting communications systems involving pilot symbols, particularly inlow signal-to-noise ratio conditions.

To this end, the invention provides in accordance with a first aspect amethod of placing pilot symbols in a data stream for telecommunicationsystems, wherein the pilot symbols are spaced in time using a range ofdifferent intervals between symbols.

The distribution of pilot symbols in time is substantially fractal innature, preferably involving repetitions of irregular groupings of pilotsymbols in the data stream, with said irregular groupings of pilotsymbols themselves irregularly spaced in the data stream.

In fundamental form of the pilot symbol distribution within a datapacket, the pilot symbols are placed with irregular spacing within afirst level group (L0 level), the irregular spacing is repeated in aplurality of such L0 groups, and the L0 groups are placed with irregularspacing within a second level group (L1 level). In a preferred form, theirregular spacing between the L0 groups is repeated in a plurality of L1groups across the data packet, and the L1 groups are placed withirregular spacing within a third level group (L2 level).

Ideally, if each L0 groups has length A, each L1 group each has lengthB, and the L2 group has length C, the pilot symbol distribution isselected such that the ratio A:B is approximately equal to the ratioB:C.

For best performance, the pilot symbols extend across substantially theentirety of the data packet.

The spacing of the pilot symbols is decided in accordance with amathematical relationship, such that their positions are substantiallypredictable, but sufficiently unevenly spaced to improve the ratio ofthe pilot symbol spectrum corresponding to the most likely frequency tothat of the next most likely frequency, when compared with thatavailable from an equivalent data stream containing evenly spaced pilotsymbols.

In accordance with a further aspect, the invention provides a signalprocessing device for use in a communications system for generating adata stream for telecommunication systems, the signal processing deviceconfigured to implement the above defined method.

A fractal is a mathematical pattern that has significant structure onseveral different length scales. Fractal patterns occur frequently innature, of course, common examples being a coastline having gulfs, bays,inlets, boulders, pebbles and sand grains on different length scales, ora tree having boughs, branches and twigs on different length scales. Ina fractal structure, there is new detail at each new length scale. Onthe other hand, a square has four corners, with simple straight linesbetween those corners. There is no new detail in a square that issmaller than the square itself.

The pilot symbol pattern of the invention is thus built fromsub-patterns that are repeated at irregular intervals, thesesub-patterns themselves built up from smaller sub-patterns. Thismulti-scale structure allows a multi-scale approach to frequencyestimation, as each scale (or level) of the pilot symbol pattern is usedto find a frequency estimate. The multi-scale algorithm uses eachfrequency estimate to resolve potential aliasing errors in the nextfrequency estimate, until the most precise frequency estimate's aliasinghas been resolved. The multi-scale algorithm is computationallyefficient because is needs only find frequency estimates for a fewsimple patterns.

The invention thus provides a new class of pilot symbol patterns thatallow efficient acquisition of the data packet's time and frequency, aswell as a novel algorithm for acquisition of the time and frequencyoffset. The pilot symbol pattern is particularly robust to phase noise,as the pilot symbols, though irregular, are placed with a uniformdensity throughout the packet. Importantly, the pilot symbol patternallows the spectrum of the pilot symbols to be narrower than that of thepacket, thus reducing adjacent channel interference during acquisition.

In accordance with the invention, different pilot symbol patterns can beselected for different users, with low cross-correlation.

The method of the invention is computationally efficient when comparedto data streams containing randomly placed pilot symbols. As the pilotsymbol intervals have a mathematical relationship with each other theyare sufficiently predictable to ensure that the computational powerneeded is significantly less than that required for randomly distributedpilot symbol schemes, yet sufficiently unevenly spaced to perform theirintended function of substantially improving the signal to noise ratio.

This type of spacing of pilot symbols is therefore fractal in nature, asit is specifically formulated to afford pilot symbol analysis on aplurality of different length scales over the packet. In a preferredembodiment, the packet structure includes small groups of pilot symbols,a plurality of these small groups grouped into a medium-level group, anda plurality of these medium-level groups grouped into a high-levelgroup. At each level, then, there is a specific group structure. Thereis preferably no mathematical repetition of the group structure from onegroup level (length scale) to the next. In a preferred embodiment, thepilot symbols are spread in this pattern over the entirety, or almostthe entirety, of the signal packet.

In accordance with a further aspect of the invention, there is provideda means of acquiring the time offset and frequency of a packet of databy using pilot symbols distributed within the packet as described above.

In one embodiment, a receiver method for receiving and acquiring atransmitted signal in a communications system is provided, the signalrepresenting a data stream including data symbols and pilot symbols, themethod including the steps of:

-   -   receiving the transmitted signal and converting to a digital        signal;    -   iteratively acquiring the frequency of the signal by the        following steps:    -   based on an assumed zero phase difference between certain        relatively closely spaced pilot symbols within the data stream,        calculating a first estimate of phase and signal amplitude;    -   calculating a relatively fine frequency estimate with potential        aliasing ambiguity, based on more widely spaced pilot symbols        within the data stream;    -   using said relatively fine frequency estimate to calculate a        phase difference between said relatively closely spaced pilot        symbols, and calculating a relatively coarse frequency estimate        based on this phase difference, with no aliasing ambiguity;    -   using the calculated relatively coarse frequency estimate to        enhance the relatively fine frequency estimate by refining said        calculated phase and signal amplitude, and thus re-calculating        said relatively fine frequency estimate;    -   using said relatively coarse frequency estimate and the enhanced        relatively fine frequency estimate to resolve potential aliasing        ambiguity in the relatively fine frequency estimate; and    -   applying the enhanced relatively fine frequency estimate to the        data stream in the acquisition of the data symbols.

In another embodiment, a receiver method for receiving and acquiring atransmitted signal in a communications system is provided, the signalrepresenting a data stream including data symbols and pilot symbols, themethod including the steps of:

-   -   receiving the transmitted signal and converting to a digital        signal;    -   acquiring the frequency of the signal by the following steps:    -   a) a medium frequency estimation step;    -   b) a coarse frequency estimation step based on the result of        step (a);    -   c) a medium frequency re-estimation step based on the result of        step (b);    -   d) an adjustment to the medium frequency estimation to resolve        potential aliasing ambiguities in the medium frequency        estimation;    -   e) a fine frequency estimation step, including a calculation of        a likelihood for the selected frequency; and    -   f) an adjustment to the fine frequency estimation to resolve        potential aliasing ambiguities in the fine frequency estimation.

In a preferred form, a further step is included, of:

-   -   g) a phase and signal estimation and correction step based on        the result of step (f).

In a preferred form, a further step is included, of:

-   -   h) the removal of the pilot symbol from the data stream to        provide a data symbol output.

The receiver method may include a process for further improving thereliability of acquisition by using additional encoded pilot symbolsembedded within the data stream, the additional pilot symbols encodedwith forward error correcting codes; the process including the steps inthe receiver of:

-   i) acquiring a list of the most probable time and frequency offset    pairs ranked in order of probability;-   ii) for each said time and frequency offset pair in the list,    starting with that with the highest probability, and proceeding in    order of decreasing probability:    -   decoding the packet on the basis of that time and frequency        offset;    -   if a predetermined number of said additional encoded pilot        symbols match their prescribed values, accepting that time and        frequency offset;    -   if not, continuing to the next time and frequency offset pair in        the list.

In a preferred form, the invention involves applying the above definedreceiver method to a transmitted signal produced by the above definedpilot symbol placing method.

For greater data transmission efficiency, the receiver method may beenhanced by selecting in the data stream one or more of the pilotsymbols and replacing them with data symbols, and applying theacquisition steps based on the assumption that these selected symbolsare pilot symbols with zero value.

In accordance with a further aspect of the invention, a receiver forreceiving and acquiring transmitted signals in a communications systemis provided, the signals representing a data stream including datasymbols and pilot symbols, the receiver including functional blocks forcarrying out the steps of the above defined receiver method.

The method of the invention therefore uses an iterative process towardscoherent signal acquisition, combining frequency estimates based on an apriori assumption of coherence between pilot symbols in the smallestsubgroup, with frequency estimates based on an a priori assumption thatpilot symbols in different subgroups are independent in phase. Themethod thus calculates phase differences between the smallest subgroups,which may include aliasing ambiguities (2π ambiguities). This phasedifference can then be used to recalculate the offset between pilotsymbols in the smallest group, allowing the resolution of any aliasingambiguities.

In a preferred three-level process, the coarsest frequency estimate isused to resolve aliasing ambiguities in an intermediate frequencyestimate, and the intermediate frequency estimate is used in turn toresolve aliasing ambiguities in the finest frequency estimate. As aresult, the pilot symbols can be summed coherently to find the correctfrequency.

The method of the invention thus relies upon the estimation of just asmall number of phase differences, one phase difference corresponding toeach layer of the multi-scale (fractal) pattern of pilot symbols.

It is to be noted that the prior art uses both UWs and pilot symbols todetermine and achieve the functions of signal acquisition (whichrequires coarse timing estimates), and determination of the correctfrequency. In contrast, the invention preferably uses pilot symbolsalone to perform both these functions, substantially all pilot symbolsbeing used to acquire both timing and frequency. The invention lendsitself to a system capable of performing both functions using pilotsymbols alone, rather than depending on contiguous blocks of consecutivesymbols making up the UWs. In particular, the timing acquisitionfunction is effectively distributed through the non-equispaced pilotsymbols.

The invention provides pilot symbol patterns shown to have bettersidelobe suppression than those of the prior art, to which acomputationaly efficient acquisition algorithm can be applied. Therelatively regular structure of the pilot symbol pattern of theinvention allows a rapid calculation of the data packet's most likelyfrequency, while the irregular intervals assist in reducing thesidelobes.

The present invention is demonstrated to have superior packet error rateperformance, using less ‘overhead’ data, thus improving the effectivethroughput data rate. A reduction in the signal to noise ratio allowslower signal power or greater symbol rate, whilst the use of a largerbandwidth allows more effective pre-processing of the incoming data.

The present invention therefore provides improved reliability ofacquisition of a data packet in the presence of noise, fading factors,or other deleterious effects. In comparison with prior art approaches itinvolves a smaller cost in pilot symbols and/or improved acquisitionover a broader bandwidth. The invention can be applied to sub-carrierbased modulation systems (OFDM) and TDMA systems, for example. Inaddition, it can be applied to block-based estimators for short-packetdata streams and sliding-window estimators for long-packet or continuoustransmission data streams.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the invention may be obtained from aconsideration of the following detailed description of a preferredembodiment, in conjunction with the accompanying drawings, in which:

FIG. 1 schematically illustrates the placement of pilot symbols within adata packet in accordance with the invention;

FIG. 2 illustrates the receiver acquisition process of a signal, inaccordance with the invention;

FIG. 3 schematically illustrates the frequency response of a methodusing two contiguous blocks of pilot symbols, in accordance with theprior art;

FIG. 4 illustrates the frequency response of a method using the pilotsymbol pattern in accordance with the invention;

FIG. 5 shows the frequency response of a method using purely randomlyspaced pilot symbols;

FIGS. 6, 7 and 8 illustrate the different steps of the receiver methodof the invention, corresponding to the different functional blocks ofthe receiver architecture;

FIG. 9 shows a system block diagram of the receiver components, and

FIG. 10 is a flow chart illustrating the various stages of the method ofthe invention.

DETAILED DESCRIPTION

The communications system of this embodiment of the invention involves asource TDMA signal including pilot symbols in the stream of datasymbols, which is passed through a communications interface and receivedat a receiver. The received signal is processed to separate the pilotsymbols from the data symbols. Ideally, the time and frequency of thepilot symbols are known to the receiver (as are the pilot symbolsthemselves), so that channel estimation can be carried out on the datasymbols. The problem is that phase noise rotates the received symbols byan amount that can vary, and it is thus necessary to calculate a phaseerror correction value in order that phase error can be suppressed. Theconventional technique is to select a set of postulates definingpossible frequency errors, to generate a set of error-compensated pilotsymbols by each of said postulates, to generate a metric giving thelikelihood of the frequency error being correct, and thus to select thefrequency in accordance with this metric. Additionally, it is necessaryto correct the time alignment in the signal.

The general concept of pilot symbols and data symbols is known to theperson skilled in the art and will not be described in further detailhere.

The acquisition routine must find the frequency and time that a packetis received. The Unique Word method (UW) transmits a known data streamto assist with the task.

In the presence of noise, the frequency cannot be found perfectly. Anuncertainty principle known as the Cramer Rao Lower Bound (CRB) limitsthe precision of the frequency determination. A short UW at the head ofa transmission is not sufficiently precise, as phase drift overtime—caused by frequency errors—can cause loss of information.

One known approach is to have two UWs, one at the front and one at theend of the packet. Each UW gives a coarse frequency estimate, whilst thephase difference between the two provides a fine resolution. Althoughthis method provides a level of improvement, it is not alwayssufficiently accurate. The phase difference is ambiguous by multiples of2π radians, leading to corresponding uncertainty in the fine frequencyoffset resolution. Further improvement can be obtained—at cost ofadditional computation—by developing a list of possible frequencyoffsets, and trying each one in turn (a method known as ‘TurboSynch’).

If information were available midway through the packet, a phasedifference of 2π between the UWs would be evident, since theintermediate pilot symbol would be incorrect by π radians. It wouldrequire a larger frequency offset—with 4π radians between UWs—beforesimilar ambiguities were encountered.

A disadvantage of using only two UWs is that no information is availableto distinguish between frequency offset possibilities. Instead, as thepresent invention appreciates, a structure is required with informationon multiple length-scales. The invention provides such a structure,involving a UW based on a fractal.

Essentially, and as explained above, a fractal is a mathematical patternthat has significant structure on a plurality of different lengthscales. An example of a mathematical fractal is the Cantor set, formedby starting with the number line between 0 and 1, removing the middlethird, leaving a segment at either end, removing the middle third ofeach segment, leaving four (irregularly spaced) segments, and thencontinuing to remove the middle third of each segment. The resultingpattern is thus made up of four clumps of entries, each clump built upof four smaller clumps, and so on.

Clearly, the set of symbols in a TDMA packet is finite, so the patternis not a true fractal. The structures described below have patterns onat least three length scales, but the skilled reader will appreciatethat a distribution having two or more length scales two is embraced bythe present invention.

In accordance with fractal geometry, a fractal cannot be treated asexisting strictly in one, two, or any other whole-number dimensions.Instead, it must be handled mathematically as though it has somefractional dimension.

The UWs of the prior art are formed from contiguous blocks of pilotsymbols. The groupings in accordance with the invention and describedbelow have pilot symbols placed irregularly throughout the packet. Thispattern has information on all length-scales, so it can resolveambiguities, but the pattern repeats sufficiently regularly to deal withnoise in a methodical way. Additionally, by using pilot symbolsthroughout the packet, fading can be more reliably tracked than hithertopossible.

The pattern of pilot symbols is ideally spread across most of thepacket. The longer patterns afford more precise frequency estimates anddo not allow as much phase drift, but are less resistant to aliasing.

As described in detail in the examples below, the acquisition methodbegins with the assumption that the symbols within the smallestsub-groups are coherent. When the frequency offset is in fact large,this assumption will lead to reduced performance, and the smallestsubgroups are therefore selected to be short in order to provideresistance to large frequency offsets.

A common problem in TDMA is phase noise, in which the phase driftsslowly in a random fashion. In accordance with the method of theinvention, the pilot symbols may be used to recover the phase. Thus, thebroadest subgroups should be spread across the packet, limiting thewidest gap between pilot symbols.

In this example, the coarsest frequency estimate is used to resolvealiasing in the intermediate frequency estimate, while the intermediatefrequency estimate is used to resolve aliasing in the finest frequencyestimate. To best ensure both these aliasing problems are resolved, theintermediate length-scale should be approximately midway between theshortest groupings and the whole packet. Mathematically, if the shortestsub-patterns have length A, the intermediate patterns have length B, andthe whole packet has length C, then the ratios should be similar,A:B≈B:C

There is of course considerable scope within the present invention toselect the specific pattern of pilot symbols. Each pattern's frequencyresponse is used to give a final metric, being the ratio between themain beam's power and the highest sidelobes. The exact pattern thusdepends on factors including the level of phase noise expected, and theneed to balance aliasing problems against the precision of the frequencyestimation.

Turning to the drawings, FIG. 1 illustrates placement of pilot symbolswithin a packet of data. Each line represents a pilot symbol, and thesecan be seen as structured into groups at different levels (differentlength-scales). L0 represents a group of pilot symbols, as does L1 andL2. The L2 group includes all the pilot symbols in the packet, includingthe L1 groups. The L1 group includes the L0 group as shown.

FIG. 2 schematically illustrates the receiver acquisition process of asignal with unknown frequency 21. The acquisition process involves,firstly, an approximation of the medium frequency estimate using the L1group (involving several sub-steps), followed by a coarse frequencyestimate using pilot symbols within the same L0 group, followed by afine frequency estimate using the L2 group. The coarse frequencyestimate is referenced in the diagram at 22, the medium frequencyestimate using pilot symbols within the L1 group, to resolve the 2πambiguities, at 23, and the fine frequency estimate—using coherentsumming of all pilot symbols within the L2 group—at 24. The acquisitionprocess is described in further detail below.

The frequency response of a pattern of pilot symbols may be defined byforming a vector of numbers, with length equal to the packet length,placing a 1 in each entry that corresponds to a pilot symbol, and a 0 inall other entries, that correspond to data symbols. The frequencyresponse is then the Fourier transform of this vector. In this way, FIG.3 illustrates the frequency response of two contiguous blocks of pilotsymbols (the absolute values of the Fourier coefficients), in accordancewith the prior art approach, whilst FIG. 4 illustrates the type offrequency response achievable by the method of the present invention.For comparison, FIG. 5 shows the typical frequency response of a methodusing purely randomly spaced pilot symbols. This illustrates a strongcentre frequency, but at the cost of very high computational load.

The procedure therefore involves three particular levels of frequencyestimation. The first provides a coarse frequency estimate with noaliasing. The last provides a precise frequency estimate with muchaliasing. The frequency estimate from the intermediate level providesintermediate precision with some (but little) aliasing. Critically, thethree phase differences have to be used to calculate three frequencyestimates (referred to as the coarse, intermediate and fine frequency)and then combined into a single, unambiguous frequency estimate.Initially, both intermediate and fine frequency estimates have aliasing.

The steps are as follows:

-   -   Set the coarse phase difference to zero.    -   Estimate the intermediate and fine phase differences.    -   Feed back the intermediate and fine phase differences to        re-estimate the coarse phase difference, and hence the coarse        frequency.    -   Re-estimate the intermediate phase difference. Use the coarse        frequency to resolve the intermediate frequency aliasing.    -   Re-estimate the fine phase difference. Use the intermediate        frequency estimate to resolve the fine frequency aliasing.

The following section describes this process and steps toward coherentsignal acquisition in more detail with reference to the figures. In thissection, specific terms are herein defined as:

-   -   “TREAT”—to algorithmically summate (add together)    -   “USE or USING”—to apply determined phase correction factor.        STEP 1—as Illustrated in FIG. 6.

TREAT pilot symbols in same L0 as coherent in phase. It is thus assumedat this step that adjacent pilot symbols in an L0 group are mutually inphase, so can be coherently summed to produce the phase estimate, inorder to reduce noise.

TREAT pilot symbols in different L1 as independent in phase. Estimatephase differentials at the L1 level.

The result of this step is α,β,γ, the phase differences between L0groups within each L1 group. It should be noted that this may include 2πambiguities, as referred to above.

STEP 2—as Illustrated in FIG. 7.

TREAT pilot symbols in each L1 group as coherent in phase USING theresults of STEP 1.

TREAT pilot symbols in different L1 groups as independent in phase.

In this way, the method therefore allows coherent combination of thefour L0 groups as the α,β,γ is repeated within the four groups. Thiscombination again reduces the effect of noise, and is of courseinsensitive to any 2π ambiguities.

Estimate phase differentials for L0.

USE this to resolve 2π ambiguities from STEP 1.

Repeat for φ and ψ

The result of this step is phase differences a, b & c, resolving any 2πambiguity in α, β, and γ.

STEP 3—as Illustrated in FIG. 8.

TREAT pilot symbols in the same L1 as coherent in phase USING theresults of STEPS 1 and 2.

Estimate phase differentials at the L2 level.

USE the results of STEPS 1 and 2 to resolve 2π ambiguities to computefrequency.

Use Ae^(jθ), Be^(jφ), Ce^(jψ) to estimate the phase differences betweenL1 blocks.

These phases can then be used to improve the medium resolution frequencyto yield a fine resolution frequency.

STEP 4

Strip the frequency offset found in STEP 3 from all pilot symbols in thepacket.

Sum the pilot symbols coherently in order to estimate the signalamplitude of the frequency determined in STEP 3.

If the signal amplitude surpasses a threshold level, strip the finefrequency offset estimate from the data symbols. The data symbols arethen output from the acquisition routine.

A system block diagram is shown in FIG. 9. The received signal is passedthrough an Analogue Digital Converter 901, then filtered by filtermodule 902, and passed to receiver acquisition block 903, giving anoutput synchronised data symbols for further processing.

A flow chart outlining the receiver acquisition process according to thepreferred embodiment is provided in FIG. 10.

The first step is symbol time estimation. The upsampled data stream isinput at functional block 1001. The data is over-sampled, andinter-symbol samples tend to be lower power than on-symbol samples, sothe data set is used to estimate the fine time-offset. The output isthen used to down-sample the packet at functional block 1002, to outputthe downsampled data stream.

The next step is the coarse time estimation at functional block 1003.The procedure for frequency estimation (see below) is followed for eachpossible time offset. A likelihood score is found for the most likelyfrequency at each time offset. The time and frequency with the mostlikely response is then selected.

The following describes the frequency estimation at a given time offset.At functional block 1004 the samples in the data stream are selectedthat correspond to pilot symbols, assuming the given time offset iscorrect, the output being 64 complex numbers. Next, an initial mediumfrequency estimate is formed at functional block 1005, assuming thecoarse frequency offset is zero. This is done by summing symbols withineach L0 group, and using differential decoding within each L1 group tofind an initial medium frequency estimate. This will be ambiguous, andwill be degraded by the poor coarse frequency estimate. The coarsefrequency is estimated at functional block 1007, using the initialmedium frequency estimate to assist (functional block 1006). The mediumfrequency estimate is used to coherently sum corresponding pilot symbolsfrom different L0 groups. This helps to measure phase differences withinL0 groups, and thus obtain a coarse frequency estimate.

The output is thus the coarse frequency estimate f_(c), and the mediumfrequency f_(m) can now be re-estimated, using the coarse frequencyestimate to assist, at functional block 1008. The technique involvesfirstly using f_(c) to sum pilot symbols coherently within each L0group, and the phase differences between L0 groups in each L1 are thenused to estimate f_(m). Then, f_(c) is used to resolve aliasing inf_(m).

The next step is the estimation of the fine frequency f_(f), using f_(c)and f_(m) to sum pilot symbols coherently within each L0 and L1 group,at functional block 1009. A fine frequency estimate is then found atfunctional block 1010 from phase differences between L1 groups. Finally,f_(c) and f_(m) are used to resolve aliasing in the fine frequencyestimate (functional block 1011) to arrive at an unambiguous finefrequency estimate f_(f).

The next step is the estimation of signal phase, power and SNR. The finefrequency is stripped from the pilot symbols at functional block 1012.The output of this step is then averaged, the amplitude of the resultgiving the likelihood score, affording phase estimation and correction(functional block 1013). The square of the amplitude gives the signalpower. The phase is recorded, as it needs to be removed from the wholepacket. The variance of the stripped pilot symbols estimates the Noiseto Signal ratio. These steps are represented by functional blocks 1014and 1015.

The output is thus the signal phase, power and SNR, for the that coarsetime offset.

The final step is to acquire the whole data packet. The coarse timeoffset is selected that maximises output power, and the symbols thatcorrespond to this time offset are selected from the data stream. Theestimated phase, frequency and power are stripped from all these symbols(functional block 1016), and the output is thus the normalised datasymbols.

Determine the Fractal Placement of the Pilot Symbols

Clearly, the invention embraces a variety of different pilot symboldistributions across a packet, the actual pattern depending on a numberof different factors of relevance. Some factors to be considered indetermination of the pattern include:

-   -   1. Choose patterns for the groups at each level (L0, L1, L2, . .        . ) to minimise the frequency response of the incorrect        frequency offset estimates.    -   2. The fractal pattern selected depends on the overall length of        the packet, therefore is scaleable for different packet lengths.    -   3. The fractal pattern selected depends on the total number of        pilot symbols within a packet.    -   4. The fractal pattern selected depends on the frequency        bandwidth under consideration.

All the above requirements give rise to different patterns of pilotsymbols chosen and implemented.

Performance Comparison with Prior Art Techniques

The comparison is made in terms of packet error rate performance. Asmentioned above, prior art approaches generally use UWs plus pilotsymbols to assist in the acquisition and frequency determination of thedata stream, and therefore includes an ‘overhead’ in addition to thereal data being transported. The current invention performs 0.5 db-1.0db better when compared to the prior art using the same number of pilotsymbols plus UW overhead. That is to say, for a given number of pilotsymbols (only) as overhead, the invention displays superior performance,by 0.5 db-1.0 db.

Implementation Efficiency

The implementation issues include:

-   -   Maintaining low manufacturing costs through low cost        computational powered digital processing integrated circuits.        (i.e. lower priced DSP, microprocessor, FPGA or other related        computing integrated circuits.)    -   Maintaining or improving on the high performance in packet error        rate figures    -   Maximising the effective data rate throughput by maintaining or        lowering the ‘overhead’ data.

The current invention has benefits in producing a data delivery systemwith reduced manufacturing costs, high performance, and low dataoverheads.

Application of the System

This invention or system of applying Fractal pilot symbols can beapplied to sub-carrier based modulation systems (eg. MCM/OFDM), FDM,WDM, and Single-Carrier TDMA systems.

In addition, the methods described apply to block-based estimators forshort-packet sized data streams and sliding-window estimators forlong-packet or continuous transmission data streams.

DETAILED EXAMPLE

The following provides a more detailed example of a packet structure:

-   -   400 Symbols    -   36 Pilot Symbols    -   Frequency offset up to 5 percent of the symbol rate        -   ->Bandwidth F=2*5%=10% of symbol rate

The number of levels in the structure depends on the number of pilotsymbols. This embodiment employs three levels, but fewer or more levelsare possible. This embodiment features three pilot symbols per L0 block,three L0 blocks per L1 block, and four L1 blocks in the full L2 block,giving a total of 36 pilot symbols in the packet. The scale factor (iethe number of Ln blocks per L(n+1) block) at each level should beideally between 3 and 6, in order to achieve the desired irregularity,and the product of the scale factors equals the total number of pilotsymbols allowed.

The acquisition process is better adapted to distinguishing coarse-time(CT) offsets than to distinguish frequency offsets. The CT acquisitionperforms early stages of the frequency acquisition, repeated for severaldifferent time-offsets. Making the early stages faster speeds up theacquisition. An L1 block with few pilot symbols is quicker to computethan one with more pilot symbols, so this embodiment speeds the wholeacquisition algorithm by choosing small scale factors for L0 and L1, asmentioned above.

Each L0 block has its Pilot Symbols at positions

-   -   (n, n+1, n+3).

Each L1 block has its L0 blocks starting at positions

-   -   (m, m+7, m+19).

The L1 blocks start at positions

-   -   (k, k+60, k+240, k+360)        Fine Structure

The first step in the algorithm assumes the symbols within each L0 blockare coherent. There is a frequency offset of up to 1/20 cycle persymbol, so an L0 block should not cover more than four symbols. The L0should be as long as possible subject to that restriction, as a longerL0 block will provide a better coarse frequency estimate than a shorterL0 block. For these reasons, the positions (n, n+1,n+3) were chosen forthe L0 structure. That is, if an L0 block starts at position n, thensymbols at positions n, n+1 and n+3 will be pilot symbols. This willallow the pilot symbols to distinguish between comparatively largefrequency offsets.

Medium Structure

The L1 group contains three L0 blocks. The L1 group needs to besufficiently wide to give a moderately precise frequency estimate, butthe L0 blocks need to be sufficiently close, and sufficiently unevenlyspaced, so that all wrong frequencies (within the scope of the coarsefrequency estimate) provide a weak response when compared with thecorrect frequency. This embodiment satisfies these requirements byplacing the L0 blocks starting at symbols (n, n+7, n+19). This permitsthe pilot symbols to distinguish between frequencies that are separatedby a moderate amount.

Coarse Structure

The full L2 group contains four L1 blocks. The full width of the L2group needs to cover most of the packet, as a longer L2 allows moreprecise frequency estimation. The L1 blocks need to be spaced unevenly,in a way that all wrong frequencies (within the scope of the mediumfrequency estimate) provide a weak response when compared with thecorrect frequency. This embodiment places the L1 blocks starting atpositions n,n+60, n+240 and n+360. The reason for this choice is to haveL1 block-pairs separated by 60, 120, 180, 240, 300, and 360 symbols,this range of separations making the pilot symbols pattern effective atdistinguishing finely between the possible frequencies.

Metric for Selecting Symbol Pattern

Suppose a pattern of pilot symbols has been chosen. This sectiondescribes a suitable method of evaluating the selected pattern, and theoperator can then—given the number of pilot symbols and the packetlength—evaluate a range of potential fractal patterns.

As a mathematical formalism, we form a vector that represents a packetof data, one entry per symbol. Place a 1 in each entry that represents apilot symbol, and a zero in the other entries that represent datasymbols.

We obtain the frequency response by taking the Fourier Transform of thevector. Restrict this FT to frequencies within a specified FrequencyBandwidth (here F=2×5%=10%) of the zero frequency. The correct frequencyoffset in this case is zero, and the corresponding Fourier coefficientwill present the greatest magnitude. The second-largest Fouriercoefficient, within the Frequency Bandwidth F of the zero offsetfrequency, is the most likely to cause a frequency error. Let R be theratio between the magnitude of the first and second Fourier CoefficientsR=abs (Largest Fourier Coefficient)/abs (Second-Largest)

The higher this ratio R, the better the pattern is for acquiring thesignal frequency.

The following symbol positions, for example, are chosen to place 36Pilot Symbols within a 400-symbol packet.

-   10+[0,1,3,7,8,10,19,20,22, 60,61,63,67,68,70,79,80,82,    240,241,243,247,248,250,259,260,262,    360,361,363,367,368,370,379,380,382]    Detailed Analysis of Errors:

The invention uses a substantially fractal pilot symbol distribution. Analgorithm for time and frequency acquisition is discussed and analysedbelow.

Definition of Fractal Pattern:

The pilot symbol pattern includes an irregular collection of samples.Their indices within the packet area _(—) {ijk}=iq+pv[j]+w[k]for i=1 . . . C, j=1 . . . M, k=1 . . . F

There are C*M*F Pilot Symbols (PS) in the packet.

The vectors v and w are irregularly spaced integers. For example,

-   -   v=[0,1,5,8,10]    -   w=[0,1,4,6]    -   p=9** this might change for 20 ms packet **    -   q=100    -   C=6 large groups    -   M=5 small groups per large group    -   F 4 PS per small group

The pilot symbols may also include BPSK values.

On a fine scale, the PS's have a pattern given by the vector w. On anintermediate scale, groups of F PS's are arranged in a pattern given bythe vector v, on a scale that is p times larger. On a large scale, thegroups of F*M PS's are spaced evenly along the packet, to allow thefading to be tracked.

The analysis will also involve the following numbers:σ²=AWGN power/Signal PowerF ₂ =F(F−1)/2M ₂ =M(M−1)/2Technique:

-   -   1. For a given time offset, select the samples that form the        pilot symbols. Strip the BPSK symbol values from these samples.    -   2. Sum all symbols within each smallest group. This will        diminish the noise by approximately, 5 dB, depending on the        pilot symbol arrangement and on the frequency offset.    -   3. Use differential decoding to get a medium-resolution        frequency estimate with moderate ambiguity problems. In this        step, the fine time offset is also estimated.    -   4. Strip the medium frequency estimate from the pilot symbols.        Apply steps similar to 2 and 3 to yield a coarse-resolution        frequency with negligible ambiguity problems.    -   5. Combine the medium and coarse frequency estimates to give an        ambiguity-free, medium resolution frequency.    -   6. Strip this frequency from the pilot symbols. Sum symbols        coherently within each medium-sized group. This will further        diminish the noise, and allow estimation of a fine frequency        offset. Use the medium frequency to resolve the ambiguity in the        fine frequency offset estimate.    -   7. Track the phase and power through the packet using a moving        average of the pilot symbols.        Analysis:

There are a number of possible sources of error:

a) Incorrect Fine Time estimate.

b) Inaccurate frequency offset estimation (medium frequency estimate).

c) Inaccurate frequency offset estimation (coarse frequency estimate).

d) Incorrect ambiguity selected after combining medium and coarsefrequency offset estimates.

e) Inaccurate frequency estimation (fine frequency estimate).

f) Incorrect ambiguity selected when combining medium and fine frequencyoffset estimates.

There is also a potential for degradation caused by the initialfrequency offset and by intermediate frequency estimation errors.

The variance in frequency will then be estimated on the assumption thatnone of the above errors occur.

The PS within each small group, and the small groups within each mediumgroup are assumed spaced in a specific irregular manner. The mediumgroups will be placed evenly within the packet to allow the fading to betracked.

Clarification of Error Sources:

The incorrect Fine Time alignment estimate is self-explanatory.

When a frequency offset is estimated using a short FFT, the frequencyoffset may either be off by a small amount, as the local maximum isshifted, or it may be off by a large amount when the wrong Fouriercoefficient is chosen. Errors d) and f) are caused by errors of theformer type; errors b), c) and e) are errors of the latter type.

The coarse frequency estimate is used to resolve ambiguities in themedium frequency estimate. However, since there is a variance associatedwith both estimates, there is a possibility that the wrong ambiguitywill be chosen, giving errors of type d) and f).

In several time slots, data symbols may present as if they werecoherent. Any frequency offset causes a temporary loss in signal tonoise ratio and ‘permanent’ loss in probability of acquisition.

Concrete Formulae:

The formulae used to estimate the fine time and variance are given inthis section. Their variances and likelihood of error will be found inthe next section.

Let the data stream be u_t, where t is measured in units of the symbolrate. We assume 4 times oversampling, so samples occur at quarter-units.s _(—) {ijk;t}=u _(—) {qi+pv(j)+w(k)+t} are the pilot symbols when thetime-offset is t.a _(—) {ij;t}=sum_(—) k s _(—) {ijk;t} R(k)b _(—) {ijk;t}=a _(—) {ij;t} a* _(—) {ik;t}c _(—) {j−k;t}=sum_(—) i b _(—) {ijk;t}d _(—) {j−k;t}=abs(c _(—) {j−k;t})^2e _(—) t=sum_(—) j d _(—) {j;t}t _(—)0=argmax(e _(—) t)=: FineTimeS _(—) {ijk}=s _(—) {ijk;t _(—)0}A _(—) {ij}=a _(—) {ij;t _(—)0}B _(—) {ijk}=b _(—) {ijk;t _(—)0}C _(—) {j−k}=c _(—) {j−k;t _(—)0}θ=argmax FFT(C _(—) {j})MediumFreq=θ/2/π*SymbolRate/p (ambiguity SymbolRate/p)Strip the Medium Freq from the UW S, to give S. This forces S_{ijk} tohave a phase that is independent of the j value (except for noise).D _(—) {ik}=sum_(—) j S _(—) {ijk}E _(—) {ijk}=D _(—) {ij} D* _(—) {ik}F _(—) {j−k}=sum_(—) I E _(—) {ijk}φ=argmax FFT(F _(—) {j})CoarseFreq=φ/2/π*SymbolRate (ambiguity SymbolRate)Use CoarseFreq to Resolve the Ambiguity in MediumFreq

Strip the ambiguity correction from the pilot symbols S, to give {hacekover (S)}. This forces {hacek over (S)}_{ijk} to have a phase that isindependent of the j and k values.G _(—) i=sum_(—) {jk} {hacek over (S)} _(—) {ijk}ψ=argmax FFT(G _(—) {i})FineFreq=ψ/2/π*SymbolRate/q (ambiguity SymbolRate/q)Use MediumFreq to Resolve the Ambiguity in FineFreq.

The phase and power may now be tracked using a moving average of thePS's, as they are fairly evenly spaced along the packet.

Background Distributions:

Some estimates are needed that are extremely complex to calculate usingcalculus.

For these purposes, curve-fitting was applied to simple situations inMatlab.

Mean and Variance of the Power of a random Gaussian:

Let z=1σn can be a complex Gaussian random variable, with mean 1 andstandard deviation σ². Note that complex random variable, n, is zeromean with unit variance.

ThenMeanPower(σ²)=mean(abs(z ²))=1+σ²VarPower(σ²)=var(abs(z ²))=2σ²+σ⁴

Estimating the maximum power of a set of complex Gaussians:

Let {a_(n)} be a collection of T complex Gaussians with zero mean andunit variance.

Let the maximum power be x=max_(n) abs(a_(n))². Then x is a random realnumber. By curve-fitting in Matlab, x has mean:MeanMaxPower(T)=0.575+log T+3/(6T+1)and variance:VarMaxPower(T)=1.65−3T/(3T ²+2)

Loss of Power due to Frequency Offset:

When N pilot symbols with a frequency offset f are summed coherently,the gain in power isIncoherentPowerLoss(f)=abs(mean_(—) n exp(jw(n) 2πf/F _(Sym))²,where w(n) is the position of the nth PS within the packet. This has amaximum value of 1 when the frequency offset f is zero.

Estimating the probability of the attributes of an FFT (variance andlocation of maximum peak in the spectrum) being correct:

Suppose T terms contribute to an FFT, each of the form exp(jn θ)+σm_(n),where m_(n) are complex Gaussian random numbers with unit variance. TheFFT will have T independent coefficients. The correct frequency estimatewill give a mean power ofFFTcorrectMeanPower(σ² ,T)=T ² MeanPower(σ² /T)and varianceFFTcorrectVarPower(σ² ,T)=T ⁴VarPower(σ² /T)

The incorrect frequency offset estimates will yield, we assume, T−1independent random complex numbers with interpolations. Each of the T−1numbers has mean zero and varianceFFTvariance=T(1+σ²).Hence their mean power isFFTmeanPower=T(1+σ²)and the variance in their power isFFTvarPower=T ²(1+σ²)².The strongest of the incorrect frequencies will have power of meanFFTmeanMaxPower=FFTmeanPower+FFTvariance*MeanMaxPower(T)and varianceFFTvarMaxPower=FFTmeanPower²*VarMaxPower(T).

Therefore the correct frequency will be chosen, and θ will be roughlycorrect, with a safety margin of this many standard deviations:FFTcorrectSD(T,σ²)=(FFTcorrectMeanPower−FFTmeanMaxPower)/sqrt(FFTcorrectVarPower+FFTvarMaxPower)

Estimating the variance of an estimated frequency:

The variance of f, assuming the correct option emerges from the FFT, is:FFTfreqVar(T,σ ²)=F _(Sym) ²σ²/(6T ³)

Estimation of Variance, and Error Probabilities:

Suppose the data has unit power and the AWGN has power σ².

We require the distribution of the estimate for the correct time offset,and also for the incorrect time offsets. The notation A˜N(B,C) is used,to mean that A is a random variable with mean B and variance C. This isnot necessarily Gaussian, although a Gaussian distribution is assumedfor this analysis. It will normally be clear from the context whether anumber is real or complex.

Estimation of Error Probability in Fine Time

At the correct fine time estimate, with the correct pilot symbolstructure, the variables will have the following distributions.

-   S_{ijk}˜N(1,σ²)-   A_{ij}˜N(F,Fσ²) % with power loss-   B_{ijk}˜N(F²;2F³σ²+CF²σ⁴)-   C_j˜N(CF²,2CF³σ²+CF²σ⁴)-   D_j˜N(C²F²+2CF³σ²+CF²σ⁴,-   E˜N(M₂(C²F²+2CF³σ²+CF²σ⁴),

At the wrong times, or with the wrong pilot symbol structure, the dataand AWGN are indistinguishable.

-   S_{ijk;t}˜N(0,1+σ²)-   A_{ij;t}˜N(0,F(1+σ²))-   B_{ijk;t}˜N(0, F²(1+σ²)²)-   C_{j;t}˜N(0, CF²(1+σ²)²)-   D_{j;t}˜N(CF² (1+σ²)²,-   E_t˜N(M₂ CF² (1+σ²)²,-   Max E˜N(+(log T+0.57), 1.65*)

Thus we might estimate the probability of error in terms of standarddeviations:(M1−m2)/sqrt(v1+v2)

The medium frequency offset is now stripped from the packet. Considerone medium group of PS, which contains M fine groups of F PS each. Thefirst PS in each fine group should now be in phase, and can be addedtogether coherently. The same applies to the second in each group, andso on. It is therefore possible to use a similar procedure for findingthe coarse frequency estimate as described above to find the mediumfrequency estimate. Although the variance of the coarse estimate isgreater, its ambiguity is much greater again, and this can be used tocorrect the ambiguity in the medium frequency.

The probability of choosing the incorrect ambiguity depends on thevariance of the Coarse and Medium Frequency estimates.

Correct the estimate for the adjusted Medium Frequency. Now all the PSwithin each medium group may be summed coherently. Each medium groupyields a single value with quite low noise, of mean value MF andvariance MFσ². These are spread evenly over the packet, and may be usedto estimate the frequency with very low variance.

The ambiguity in this estimate is the Symbol Rate divided by the spacingbetween medium groups. The adjusted medium frequency is used to resolvethe ambiguity in the Fine Frequency.

The inventor of the present invention has carried out performancecomparison between use of a pilot symbol distribution in accordance withthe invention and use of a comparable distribution in accordance withthe patterns proposed in the Lo, Lee and Gansman IEEE paper referencedabove, specifically patterns M01, M02 and M013 shown in FIG. 1 of thatpaper. These arrangements add three pilot symbols to the purely uniformpattern U10. It is to be noted that pattern M03 has the disadvantage, asdemonstrated in FIG. 5 of the paper, that it cannot correct Dopplershifts beyond a certain limit, due to aliasing problems. In contrast,the fractal pattern is devised to be able to handle Doppler shifts usingsparse pilot symbols. In order to carry out a like-for-like comparison,patterns were simulated based on M01, M02 and M03 by pattern repetition,to form packets with around 70 pilot symbols in a packet length orapproximately 500 symbols. These could then be compared with theperformance of a fractal pattern of 500 symbols including 64 pilotsymbols. Fading was added with a frequency bandwidth equal to 40% of thepacket frequency. Fading causes power changes within each packet,although the power change caused by fading is 0 dB when averaged overthe whole packet.

The results of this comparison, in various noise levels, were that thebest pattern (in terms of probability of acquisition in a Dopplerfrequency offset) is the fractal pattern. In addition, the fractalpatterns used included fewer pilot symbols than the other patternsanalysed (64, as compared with 70).

The examples described above and in the accompanying figures aredirected to fractal patterns having three levels or length scales, andacquisition algorithms designed to acquire signals containing such pilotsymbol arrangements. As noted above, patterns over other numbers oflength scales are possible. For example, for smaller data packets withfewer pilot symbols, two-level fractal patterns may be more appropriate.This can give better sidelobe reduction, but needs more computation thana three-level method for the same number of pilot symbols.

For a two-level fractal pattern (ie, containing a plurality of L0 groupswithin an L1 group spanning the packet length), the acquisitionalgorithm does not require an intermediate frequency estimate. Theacquisition steps are therefore:

-   a) A fine frequency estimation step, assuming the coarse frequency    offset is zero;-   b) A coarse frequency estimation step based on the result of step    a);-   c) A fine frequency re-estimation step based on the result of step    b); and-   d) An adjustment to the fine frequency estimation to resolve 2π    ambiguities in the fine frequency estimation.

A further alternative embodiment of the present invention involvesreplacing one or more pilot symbols of the fractal pattern with datasymbols, to provide a ‘punctured’ fractal pilot symbol pattern, and thenapplying the acquisition process of the invention, making the assumptionthat these pilot symbols have zero value. This can increase theefficiency in terms of rate of data transmission, particularly insituations of high SNR. In this variant, then, the pilot symbol patternis not strictly fractal, but the acquisition technique designed forfractal structures—albeit with minor adjustment—can be employed.

Reference is made above to the known so-called ‘TurboSynch’ technique inTDMA. Such a technique might also be combined with the acquisitionmethod of the present invention, to provide further improvement to thereliability. In this method, the data is encoded with forward errorcorrecting codes such as turbo codes, before insertion into the datastream. In application, the steps of such a method involve:

embedding further pilot bits within the data before transmission;

encoding the result with forward error correcting codes;

in the receiver, acquiring a list of the few most likely time andfrequency offset pairs, ranked in order of likelihood; and

for each time and frequency offset pair in the list, starting with themost likely, and proceeding in their order of likelihood,

-   -   decoding the packet based on the assumption of that time and        frequency offset;    -   if enough of the embedded pilot bits match their prescribed        values, accepting that time and frequency offset; and    -   otherwise continuing until the embedded pilot bits are found to        match their prescribed values or until the list is exhausted.

The functional steps of the method of the invention can be implementedon a digital signal processing chip, or with software on a suitablecomputer apparatus.

It is to be understood that the above description of preferredembodiments of the present invention is not limitative of the scope ofthe invention, as variations and additions are possible withoutdeparting from the spirit of the invention.

1. A method of placing pilot symbols in a data stream fortelecommunications systems, the data stream including a data packet,comprising: placing the pilot symbols with irregular spacing within afirst level group; repeating the irregular spacing in a plurality ofsuch first level groups; placing the first level groups with irregularspacing within a second level group; and wherein the pilot symbols aredistributed within the data stream in time in a manner fractal in natureusing a range of different intervals between the pilot symbols.
 2. Themethod of claim 1, wherein the distributing further includes: repeatingthe irregular spacing between the first level groups in a plurality ofsecond level groups across the data packet; and placing the second levelgroups with irregular spacing within a third level group.
 3. The methodof claim 2, wherein each first level group has length A, each secondlevel group has length B, and the third level group has length C, thepilot symbol distribution selected such that the ratio A:B isapproximately equal to the ratio B:C.
 4. The method of claim 1, whereinthe pilot symbols extend across the entirety of the data packet.
 5. Asignal processing device for use in a communications system, the signalprocessing device comprising: a data source configured to generate adata stream for telecommunications systems; and a pilot symbol placerconfigured to place pilot symbols in the data stream in accordance withthe method of claim
 1. 6. A method for receiving and acquiring atransmitted signal in a communications system, the signal representing adata stream including data symbols and pilot symbols, the methodcomprising: receiving the transmitted signal and converting to a digitalsignal; and acquiring by iteration the frequency of the signal by:calculating a first estimate of phase and signal amplitude based on anassumed zero phase difference between certain closely spaced pilotsymbols within the data stream; calculating a fine frequency estimatewith aliasing ambiguity based on more widely spaced pilot symbols withinthe data stream; using said fine frequency estimate to calculate a phasedifference between said closely spaced pilot symbols, and calculating acoarse frequency estimate based on this phase difference, with noaliasing ambiguity; using the calculated coarse frequency estimate toenhance the fine frequency estimate by refining said calculated phaseand signal amplitude, and thus re-calculating said fine frequencyestimate; using said coarse frequency estimate and the enhanced finefrequency estimate to resolve the aliasing ambiguity in the finefrequency estimate; and applying the enhanced fine frequency estimate tothe data stream in the acquisition of the data symbols.
 7. A method forreceiving and acquiring a transmitted signal in a communications system,the signal representing a data stream including data symbols and pilotsymbols, the method comprising: receiving the transmitted signal andconverting to a digital signal; and acquiring the frequency of thesignal by: a) a medium frequency estimation; b) a coarse frequencyestimation based on the result of (a); c) a medium frequencyre-estimation based on the result of (b); d) an adjustment to the mediumfrequency estimation to resolve aliasing ambiguities in the mediumfrequency estimation; e) a fine frequency estimation, including acalculation of a likelihood for the selected frequency; and f) anadjustment to the fine frequency estimation to resolve aliasingambiguities in the fine frequency estimation.
 8. The method of claim 7,further comprising: g) phase and signal estimation and correction basedon the result of (f).
 9. The method of claim 8, further comprising: h)removing the pilot symbol from the data stream to provide a data symboloutput.
 10. The method of claim 8, further comprising: estimatingvariance.
 11. The method of claim 10, wherein the reliability of theacquiring is improved by using additional encoded pilot symbols embeddedwithin the data stream, the additional pilot symbols encoded withforward error correcting codes, the method further comprising: acquiringa list of the most probable time and frequency offset pairs ranked inorder of probability; starting with the highest probability, andproceeding in order of decreasing probability for each said time andfrequency offset pair in the list: decoding the packet on the basis ofthe time and frequency offset; accepting the time and frequency offsetif a predetermined number of said additional encoded pilot symbols matchtheir prescribed values; and continuing to the next time and frequencyoffset pair in the list if the predetermined number of said additionalencoded symbols do not match their prescribed values.
 12. The method ofclaim 11, wherein the pilot symbols are spaced in time using a range ofdifferent intervals between symbols.
 13. The method of claim 12,enhanced for greater data transmission efficiency, wherein one or moreof the pilot symbols in the selected data stream are replaced with datasymbols, and the acquiring the frequency of the signal is based on theassumption that these selected symbols are pilot symbols with zerovalue.
 14. A receiver for receiving and acquiring transmitted signals ina communications system, the signals representing a data streamincluding data symbols and pilot symbols, the receiver comprising: afunctional block for receiving the transmitted signal and converting toa digital signal; and a functional block for iteratively acquiring thefrequency of the signal, including: a functional block for calculating afirst estimate of phase and signal amplitude based on an assumed zerophase difference between certain closely spaced pilot symbols within thedata stream; a functional block for calculating a fine frequencyestimate with aliasing ambiguity, based on more widely spaced pilotsymbols within the data streams; a functional block for using said finefrequency estimate to calculate a phase difference between said closelyspaced pilot symbols, and calculating a coarse frequency estimate basedon this phase difference, with no aliasing ambiguity; a functional blockfor using the calculated coarse frequency estimate to enhance the finefrequency estimate by refining said calculated phase and signalamplitude, and thus re-calculating said fine frequency estimate; afunctional block for using said coarse frequency estimate and theenhanced fine frequency estimate to resolve aliasing ambiguity in thefine frequency estimate; and a functional block for applying theenhanced fine frequency estimate to the data stream in the acquisitionof the data symbols.
 15. A receiver for receiving and acquiringtransmitted signals in a communications system, the signals representinga data stream including data symbols and pilot symbols, the receivercomprising: a functional block for receiving the transmitted signal andconverting to a digital signal; and a functional block for acquiring thefrequency of the signal, including: a) a functional block for carryingout a medium frequency estimation-step; b) a functional block forcarrying out a coarse frequency estimation step based on the result of(a); c) a functional block for carrying out a medium frequencyre-estimation step based on the result of (b); d) a functional block forcarrying out an adjustment to the medium frequency estimation to resolvealiasing ambiguities in the medium frequency estimation; e) a functionalblock for carrying out a fine frequency estimation, including acalculation of a likelihood for the selected frequency; f) a functionalblock for carrying out an adjustment to the fine frequency estimation toresolve aliasing ambiguities in the fine frequency estimation.